/*
Source : https://leetcode.com/problems/unique-paths/
Author : nflush@outlook.com
Date   : 2016-07-06
*/
/*
62. Unique Paths

    Total Accepted: 93718
    Total Submissions: 253106
    Difficulty: Medium

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?


Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.
*/
class Solution {
    int cab(int a, int b){
        if (b > a-b) return cab(a, a-b);
        long int ret = a;
        for (int x = 2;x<=b;x++){
            ret = ret * (a -x + 1)/x;
        }
        return (int)ret;
    }
public:
    int uniquePaths(int m, int n) {
        if (m < n) return uniquePaths(n,m);
        if (n < 2) return n;
        if (n == 2) return m;
        return cab(m+n-2, n-1);
    }
};
